(a^(2)a^(-5))/(a^(-3)a^(0))*((a^(2))/(a^(3)))^(-4)=a^(x) What is the value of x ?

Simplify Numerator: We will simplify the expression step by step using the properties of exponents. First, we simplify the numerator and the denominator separately. (a^(2)a^(-5)) simplifies to a^(2-5) by using the property a^(m)a^(n) = a^(m+n).Simplify Denominator: Now we simplify a^(2-5) which equals a^(-3).Divide Numerator by Denominator: Next, we simplify the denominator (a^(-3)a^(0)). Since any number to the power of 0 is 1, a^(0) = 1. So, we have a^(-3)*1 which is just a^(-3).Simplify Second Part: Now we divide the simplified numerator by the simplified denominator. a^(-3) / a^(-3) equals a^(-3-(-3)) by using the property a^(m) / a^(n) = a^(m-n).Raise to Power: Simplifying a^(-3-(-3)) gives us a^(0), because -3 - (-3) equals 0. Since any number to the power of 0 is 1, a^(0) = 1.Multiply Results: Now we need to simplify the second part of the expression ((a^(2))/(a^(3)))^(-4). First, we simplify inside the parentheses: a^(2) / a^(3) equals a^(2-3) by using the property a^(m) / a^(n) = a^(m-n).Final Simplification: Simplifying a^(2-3) gives us a^(-1).Now we raise a^(-1) to the power of -4, which is (a^(-1))^(-4). Using the property (a^(m))^n = a^(m*n), we get a^(-1*-4).Simplifying a^(-1*-4) gives us a^(4).Now we multiply the result from the first part of the expression, which is 1, by the result from the second part of the expression, which is a^(4). 1 * a^(4) equals a^(4).We have now simplified the entire expression to a^(4), which means that a^(x) = a^(4). Therefore, the value of x is 4.

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(a^(2)a^(-5))/(a^(-3)a^(0))*((a^(2))/(a^(3)))^(-4)=a^(x)
What is the value of
x ?

$\frac{a^{2} a^{-5}}{a^{-3} a^{0}} \cdot\left(\frac{a^{2}}{a^{3}}\right)^{-4}=a^{x}$ $\newline$ What is the value of $x$ ?

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Algebra 1

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\frac{a^{2} a^{-5}}{a^{-3} a^{0}} \cdot\left(\frac{a^{2}}{a^{3}}\right)^{-4}=a^{x}

\newline

What is the value of

x

Simplify Numerator: We will simplify the expression step by step using the properties of exponents. $\newline$ First, we simplify the numerator and the denominator separately. $\newline$ $a^{2}a^{-5}$ simplifies to $a^{2-5}$ by using the property $a^{m}a^{n} = a^{m+n}$ .
Simplify Denominator: Now we simplify $a^{2-5}$ which equals $a^{-3}$ .
Divide Numerator by Denominator: Next, we simplify the denominator $a^{-3}a^{0}$ . Since any number to the power of $0$ is $1$ , $a^{0} = 1$ . So, we have $a^{-3}\cdot 1$ which is just $a^{-3}$ .
Simplify Second Part: Now we divide the simplified numerator by the simplified denominator. $a^{-3} / a^{-3}$ equals $a^{-3-(-3)}$ by using the property $a^{m} / a^{n} = a^{m-n}$ .
Raise to Power: Simplifying $a^{(-3-(-3))}$ gives us $a^{0}$ , because $-3 - (-3)$ equals $0$ . $\newline$ Since any number to the power of $0$ is $1$ , $a^{0} = 1$ .
Multiply Results: Now we need to simplify the second part of the expression $((a^{2})/(a^{3}))^{-4}$ . First, we simplify inside the parentheses: $a^{2} / a^{3}$ equals $a^{2-3}$ by using the property $a^{m} / a^{n} = a^{m-n}$ .
Final Simplification: Simplifying $a^{2-3}$ gives us $a^{-1}$ .
Final Simplification: Simplifying $a^{(2-3)}$ gives us $a^{-1}$ .Now we raise $a^{-1}$ to the power of $-4$ , which is $(a^{-1})^{-4}$ . Using the property $(a^{m})^{n} = a^{m*n}$ , we get $a^{(-1*-4)}$ .
Final Simplification: Simplifying $a^{(2-3)}$ gives us $a^{-1}$ .Now we raise $a^{-1}$ to the power of $-4$ , which is $(a^{-1})^{-4}$ . Using the property $(a^{m})^{n} = a^{m*n}$ , we get $a^{(-1*-4)}$ .Simplifying $a^{(-1*-4)}$ gives us $a^{4}$ .
Final Simplification: Simplifying $a^{(2-3)}$ gives us $a^{-1}$ .Now we raise $a^{-1}$ to the power of $-4$ , which is $(a^{-1})^{-4}$ . Using the property $(a^{m})^{n} = a^{m*n}$ , we get $a^{(-1*-4)}$ .Simplifying $a^{(-1*-4)}$ gives us $a^{4}$ .Now we multiply the result from the first part of the expression, which is $1$ , by the result from the second part of the expression, which is $a^{4}$ . $a^{-1}$ $1$ equals $a^{4}$ .
Final Simplification: Simplifying $a^{(2-3)}$ gives us $a^{-1}$ .Now we raise $a^{-1}$ to the power of $-4$ , which is $(a^{-1})^{-4}$ . Using the property $(a^{m})^{n} = a^{m*n}$ , we get $a^{(-1*-4)}$ . Simplifying $a^{(-1*-4)}$ gives us $a^{4}$ . Now we multiply the result from the first part of the expression, which is $1$ , by the result from the second part of the expression, which is $a^{4}$ . $a^{-1}$ $1$ equals $a^{4}$ . We have now simplified the entire expression to $a^{4}$ , which means that $a^{-1}$ $4$ . Therefore, the value of $a^{-1}$ $5$ is $a^{-1}$ $6$ .