Question

Simplify the expression.

Answer 1

D) 1/m^18

Explanation:
(m^-2/m-1m5)^3
m^-6/m^-3m^15
1/m^6 / m^15/m^3
1/m^6 / m^12
1/m^6 (1/m^12)
1/m^18

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Answer 2

Answer:

$D)\frac{1}{m^{18} }$

Step-by-step explanation:

Multiply $m^{-1}$ by $m^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} =a^{m+n}$ to combine exponents.

$(\frac{m^{-1+5} }{m^{-2} } )^{-3}$

Add -1 and 5.

$(\frac{m^{4} }{m^{-2} } )^{-3}$

Move $m^{-2}$ to the numerator using the negative exponent rule $\frac{1}{b^{-n} } =b^{n}$.

$(m^{4} m^{2} )$

Multiply $m^{4}$ by $m^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} =a^{m+n}$ to combine exponents.

$(m^{4+2} )^{-3}$

Add 4 and 2.

$(m^{6} )^{-3}$

Multiply the exponents in $(m^6)^{-3}$

Apply the rule and multiply exponents, $(a^m)^n=a^{mn}$.

$m^{6*-3}$

Multiply 6 by -3.

$m^{-18}$

Rewrite the expression using the negative exponent rule $b^{-n} =\frac{1}{b^{n} }$.

$\frac{1}{m^{18} }$