Question

$(-4a7b^{5})^{3}=(-4a7b^{5})(-4a7b^{5})(4a7b^{5})=4^{3}a^{3\times3}b^{10\times3}=64a^{9}b^{15}$

Explanation:

Step1: Correct sign handling

When multiplying three negative terms: $(-4a^7b^5) \times (-4a^7b^5) \times (-4a^7b^5) = - (4 \times 4 \times 4) \times (a^7 \times a^7 \times a^7) \times (b^5 \times b^5 \times b^5)$

Step2: Compute coefficient power

Calculate $4^3$: $4^3 = 64$, so coefficient is $-64$

Step3: Apply exponent product rule

For $a$-terms: $a^{7+7+7} = a^{21}$; for $b$-terms: $b^{5+5+5} = b^{15}$

Step4: Combine all parts

Multiply coefficient and variable terms: $-64a^{21}b^{15}$

Answer:

$-64a^{21}b^{15}$