Apply the Properties of Integer Exponents to generate equivalent expressions to 40 ⋅ 5−2(−2)−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

Question

40 ⋅ 5−2(−2)−3=

Answer 1

To apply the properties of integer exponents, we need to work step-by-step through the expression.

Step 1: Deal with the negative exponents first. In this case, we have 5^(-2) and 5^(-3). The property states that a number raised to a negative exponent is equal to 1 over that number raised to the positive exponent.

So, 5^(-2) = 1/5^2 and 5^(-3) = 1/5^3.

Step 2: Simplify any exponent expressions. In this case, we have (-2)(-2) which equals 4.

So now the expression becomes:

40 * (1/5^2)(4)(1/5^3)

Step 3: Simplify the numerical expression. 40 * 4 is equal to 160.

So the expression becomes:

160 * (1/5^2)(1/5^3)

Step 4: Simplify the exponent expression. When multiplying exponent expressions with the same base, we add the exponents.

So 5^2 * 5^3 = 5^(2+3) = 5^5.

Now the expression becomes:

160 * (1/5^5).

Step 5: Simplify the expression further. 1/5^5 means 1 divided by 5^5.

So the final expression is:

160/5^5.

This can also be written as a simplified fraction:

32/3125.

Therefore, the equivalent expression to 40 ⋅ 5^(-2)(-2)^(-3) with positive exponents is 32/3125.