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. (1 point)
To apply the properties of integer exponents, start by simplifying each exponent separately:
(5^(-3))^6 = 5^(-18)
5^17 = 5^17
10^(-2) = 1/10^2 = 1/100
Now, rewrite the expression with only positive exponents:
(5^(-3))^6 * 5^17 / 10^(-2)
= 5^(-18) * 5^17 / 1/100
= 5^(-18) * 5^17 * 100
= 5^(-18 + 17) * 100
= 5^(-1) * 100
= 1/5 * 100
= 20
Therefore, the simplified expression is 20.
explain pls
Certainly!
To apply the properties of integer exponents, we need to simplify each exponent separately.
Starting with (5^(-3))^6, we can rewrite it as 5^(-18) by multiplying the exponents inside the parentheses. When we raise a negative number to an even exponent, like 6, the result is a positive number.
Next, we have 5^17. This is already in a simplified form.
Similarly, we have 10^(-2) in the expression. To simplify this, we can rewrite it as 1/10^2 by using the rule that when we have a negative exponent, it can be flipped to the opposite sign in the denominator.
Now, we can rewrite the expression with only positive exponents:
(5^(-3))^6 * 5^17 / 10^(-2) :
= 5^(-18) * 5^17 * 1/10^2 :
= 5^(-18 + 17) * 1/10^2 :
= 5^(-1) * 1/10^2 :
= 1/5 * 1/10^2 :
= 1/5 * 1/100 :
= 20
Therefore, the simplified expression is 20.