Question

(а^-2)^3×а^5×5/а^-7×а^4

Answer 1

$(a^{ - 2} )^{6} \times a^{5} \times \frac{ 5 }{ {a}^{ - 7} } \times {a}^{ -4} = {a}^{ - 12} \times {a}^{5} \times 5 \times {a}^{7} \times {a}^{4} = \frac{1}{ {a}^{12} } \times 5 \times {a}^{16} = 5 \times {a}^{4}$

Answer 2

To simplify the expression (а^-2)^3 × а^5 × 5 / а^-7 × а^4, we can apply the rules of exponents.

First, let's simplify the exponentiation:

(а^-2)^3 = а^(-2 × 3) = а^-6

Now, let's rewrite the expression using the simplified terms:

а^-6 × а^5 × 5 / а^-7 × а^4

Next, we can combine the terms with the same base by adding their exponents:

а^-6 × а^5 × 5 / а^-7 × а^4 = а^(-6 + 5) × 5 / а^-7 × а^4

Simplifying further:

= а^-1 × 5 / а^-7 × а^4

To divide exponential terms with the same base, we subtract the exponent of the denominator from the exponent of the numerator:

= а^-1 × 5 / а^-7 × а^4 = а^(1 - (-7)) × 5 × а^4

= а^8 × 5 × а^4

Finally, we can multiply the terms with the same base by adding their exponents:

= а^(8 + 4) × 5

= а^12 × 5

Therefore, the simplified form of (а^-2)^3 × а^5 × 5 / а^-7 × а^4 is а^12 × 5.