Question

apply the properties of integer exponents to generate an equivalent expression to
(5^ -3)^6*5^17/10^-2 with only positive exponents then solve the expression

Answer 1

To generate an equivalent expression with only positive exponents, we can apply the property of negative exponents, which states that a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent:

(5^ -3)^6 * 5^17 / 10^-2

Using this property, we can convert the negative exponents:

(1 / 5^3)^6 * 5^17 * 10^2

Simplifying the expression inside the parentheses:

(1 / 125)^6 * 5^17 * 10^2

Now, let's simplify the powers:

(1^6 / 125^6) * 5^17 * 10^2

Simplifying further:

1 / 125^6 * 5^17 * 10^2

Now, we can apply the property of multiplying exponents with the same base, which states that when multiplying exponential expressions with the same base, we add the exponents:

1 / (125^6 * 5^-17 * 10^-2)

Since the exponents are all positive now, we can remove the negative signs:

1 / (125^6 * 1/5^17 * 1/10^2)

Simplifying the exponents:

1 / (244140625 * 1/762939453125 * 1/100)

Multiplying the fractions:

1 / (244140625/76293945312.5)

Dividing the numerator by the denominator:

= 76293945312.5 / 244140625

= 312500

So, the simplified expression is 312500.