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

Apply negative exponent rule: Apply the negative exponent rule. The negative exponent rule states that a^(-n) = 1/(a^n). Therefore, we can rewrite the expression as the reciprocal of the base raised to the positive exponent. ((b^(7))/(4^(5)))^(-3) = 1/((b^(7))/(4^(5)))^(3)Apply power of quotient rule: Apply the power of a quotient rule. The power of a quotient rule states that (a/b)^n = a^n / b^n. We will apply this rule to the expression inside the reciprocal. 1/((b^(7))/(4^(5)))^(3) = 1/(b^(7*3) / 4^(5*3))Multiply exponents: Multiply the exponents. We multiply the exponents inside the parentheses by 3, as indicated by the power of a quotient rule. 1/(b^(7*3) / 4^(5*3)) = 1/(b^(21) / 4^(15))Rewrite as division of powers: Rewrite the expression as a division of two powers. We can rewrite the expression as the division of b^(21) by 4^(15). 1/(b^(21) / 4^(15)) = 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)
(b^(21))/(4^(15))
C
(4^(15))/(b^(21))

Select the equivalent expression. $\newline$ $\left(\frac{b^{7}}{4^{5}}\right)^{-3}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $b^{-21}\cdot4^{-15}$ $\newline$ (B) $\frac{b^{21}}{4^{15}}$ $\newline$ (C) $\frac{4^{15}}{b^{21}}$

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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)

b^{-21}\cdot4^{-15}

\newline

(B)

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

\newline

(C)

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

Apply negative exponent rule: Apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . Therefore, we can rewrite the expression as the reciprocal of the base raised to the positive exponent. $\newline$ $\left(\frac{b^{7}}{4^{5}}\right)^{-3} = \frac{1}{\left(\frac{b^{7}}{4^{5}}\right)^{3}}$
Apply power of quotient rule: Apply the power of a quotient rule. $\newline$ The power of a quotient rule states that $(a/b)^n = a^n / b^n$ . We will apply this rule to the expression inside the reciprocal. $\newline$ $1/((b^{7})/(4^{5}))^{3} = 1/(b^{7*3} / 4^{5*3})$
Multiply exponents: Multiply the exponents. $\newline$ We multiply the exponents inside the parentheses by $3$ , as indicated by the power of a quotient rule. $\newline$ $1/(b^{7*3} / 4^{5*3}) = 1/(b^{21} / 4^{15})$
Rewrite as division of powers: Rewrite the expression as a division of two powers. $\newline$ We can rewrite the expression as the division of $b^{21}$ by $4^{15}$ . $\newline$ $1/(b^{21} / 4^{15}) = 4^{15} / b^{21}$