Select the equivalent expression. ((b^(7))/(4^(5)))^(-3)=? Choose 1 answer: (A) (b^(21))/(4^(15)) (B) (4^(15))/(b^(21)) (C) b^(-21)*4^(-15)

Understand Exponent Properties: First, we need to understand the properties of exponents. When an expression in the form of (a/b)^n is given, it can be rewritten as a^n / b^n. In this case, our expression is ((b^(7))/(4^(5)))^(-3). We will apply this property to simplify the expression.Apply Exponent Rule: Applying the exponent rule, we get: ((b^(7))^(-3))/((4^(5))^(-3)) This means we raise both the numerator and the denominator to the power of -3.Simplify Using Power Rule: Simplify the expression further by applying the power of a power rule, which states that (a^m)^n = a^(m*n). Therefore, we have: b^(7*(-3)) / 4^(5*(-3)) This simplifies to: b^(-21) / 4^(-15)Handle Negative Exponents: Now, we need to understand what it means to have a negative exponent. The rule for negative exponents states that a^(-n) = 1/a^n. Applying this rule to both the numerator and the denominator, we get: 1/b^(21) * 4^(15) / 1 This simplifies to: 4^(15) / b^(21)

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Select the equivalent expression.

((b^(7))/(4^(5)))^(-3)=?
Choose 1 answer:
(A)
(b^(21))/(4^(15))
(B)
(4^(15))/(b^(21))
(C)
b^(-21)*4^(-15)

Select the equivalent expression. $\newline$ $\left(\frac{b^{7}}{4^{5}}\right)^{-3}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{b^{21}}{4^{15}}$ $\newline$ (B) $\frac{4^{15}}{b^{21}}$ $\newline$ (C) $b^{-21}\cdot 4^{-15}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{b^{7}}{4^{5}}\right)^{-3}=

\newline

Choose

1

answer:

\newline

(A)

\frac{b^{21}}{4^{15}}

\newline

(B)

\frac{4^{15}}{b^{21}}

\newline

(C)

b^{-21}\cdot 4^{-15}

Understand Exponent Properties: First, we need to understand the properties of exponents. When an expression in the form of $(a/b)^n$ is given, it can be rewritten as $a^n / b^n$ . In this case, our expression is $((b^{7})/(4^{5}))^{-3}$ . We will apply this property to simplify the expression.
Apply Exponent Rule: Applying the exponent rule, we get: $\newline$ $((b^{7})^{(-3)})/((4^{5})^{(-3)})$ $\newline$ This means we raise both the numerator and the denominator to the power of $-3$ .
Simplify Using Power Rule: Simplify the expression further by applying the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . Therefore, we have: $\newline$ $b^{7*(-3)} / 4^{5*(-3)}$ $\newline$ This simplifies to: $\newline$ $b^{-21} / 4^{-15}$
Handle Negative Exponents: Now, we need to understand what it means to have a negative exponent. The rule for negative exponents states that $a^{-n} = \frac{1}{a^n}$ . Applying this rule to both the numerator and the denominator, we get: $\newline$ $\frac{1}{b^{21}} \cdot 4^{15} / 1$ $\newline$ This simplifies to: $\newline$ $\frac{4^{15}}{b^{21}}$