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2 years ago

Please explain how to solve this step by step.

Mathematics

1 answer:

Phantasy [73]2 years ago

5 0

Answer:

(a^8)/(b^9)

Step-by-step explanation:

Two rules of exponents come into play.

(a^b)/(a^c) = a^(b-c)

a^-b = 1/a^b

Applying the first rule, we have ...

(a^3)/(a^-5) × (b^-2)/(b^7) = a^(3 -(-5)) × b^(-2 -7) = a^8 × b^-9

Applying the second rule gives the simplified form ...

= (a^8)/(b^9)

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2 years ago

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A cone's volume can be found using the formula $V = \frac{1}{3} \pi r^2 h$ . If the cone has a diameter of 3 inches then its radius is half r= 1.5 inches. Substitute r = 1.5 and V = 12 cubic inches.

$V = \frac{1}{3} \pi r^2 h \\12 = \frac{1}{3} \pi (1.5)^2 h \\12 = \frac{1}{3} \pi (2.25) h\\12 = 2.355h\\5.10 = h$

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