b^3 times (b^4)^2 = b^x x =

Understand the problem: Understand the problem and the properties of exponents. We need to find the value of x in the expression b^3 * (b^4)^2 = b^x. According to the properties of exponents, when we multiply two exponents with the same base, we add the exponents. Also, when we raise an exponent to another power, we multiply the exponents.Apply power property: Apply the power of a power property to (b^4)^2. (b^4)^2 means that we multiply the exponent 4 by 2. (b^4)^2 = b^(4*2) = b^8Multiply exponents: Multiply b^3 by b^8 using the property of exponents for multiplication. Now we multiply b^3 by b^8, which means we add the exponents. b^3 * b^8 = b^(3+8) = b^11Solve for x: Set the result equal to b^x and solve for x. We have b^3 * (b^4)^2 = b^11, and this is set equal to b^x. Therefore, b^x = b^11 So, x = 11

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$b^3 \times (b^4)^2 = b^x$ $\newline$ $x=\square$

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Algebra 2

Composition of linear and quadratic functions: find a value

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b^3 \times (b^4)^2 = b^x

\newline

x=\square

Understand the problem: Understand the problem and the properties of exponents. We need to find the value of $x$ in the expression $b^3 \cdot (b^4)^2 = b^x$ . According to the properties of exponents, when we multiply two exponents with the same base, we add the exponents. Also, when we raise an exponent to another power, we multiply the exponents.
Apply power property: Apply the power of a power property to $(b^4)^2$ . $(b^4)^2$ means that we multiply the exponent $4$ by $2$ . $(b^4)^2 = b^{(4*2)} = b^8$
Multiply exponents: Multiply $b^3$ by $b^8$ using the property of exponents for multiplication. $\newline$ Now we multiply $b^3$ by $b^8$ , which means we add the exponents. $\newline$ $b^3 \times b^8 = b^{3+8} = b^{11}$
Solve for x: Set the result equal to $b^x$ and solve for $x$ . $\newline$ We have $b^3 \cdot (b^4)^2 = b^{11}$ , and this is set equal to $b^x$ . $\newline$ Therefore, $b^x = b^{11}$ $\newline$ So, $x = 11$