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Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve...Asked by Treetard
Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 x 5^-2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
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Answered by
Treetard
thanks daddy bot
Answered by
GPT 3.5
To apply the properties of integer exponents to generate equivalent expressions, we can use the following rules:
1) a^0 = 1 (any nonzero number raised to the power of zero is equal to 1)
2) a^(-b) = 1/(a^b) (a negative exponent can be rewritten as the reciprocal of the positive exponent)
Now let's apply these rules to the given expression: 4^0 x 5^-2/(-2)^-3.
1) 4^0 is equal to 1, so we can rewrite the expression as 1 x 5^-2/(-2)^-3.
2) 5^-2 can be rewritten as 1/(5^2) and (-2)^-3 can be rewritten as 1/((-2)^3), so the expression becomes 1 x 1/(5^2) / 1/((-2)^3).
Now we can simplify the expression further. In order to divide fractions, we multiply by the reciprocal of the divisor. So the expression becomes:
1 x 1/(5^2) x ((-2)^3)/1.
Simplifying the fractions and exponents, we get:
1 x 1/(25) x (-8) = -8/25.
Therefore, the simplified fraction with no remaining exponents is -8/25.
1) a^0 = 1 (any nonzero number raised to the power of zero is equal to 1)
2) a^(-b) = 1/(a^b) (a negative exponent can be rewritten as the reciprocal of the positive exponent)
Now let's apply these rules to the given expression: 4^0 x 5^-2/(-2)^-3.
1) 4^0 is equal to 1, so we can rewrite the expression as 1 x 5^-2/(-2)^-3.
2) 5^-2 can be rewritten as 1/(5^2) and (-2)^-3 can be rewritten as 1/((-2)^3), so the expression becomes 1 x 1/(5^2) / 1/((-2)^3).
Now we can simplify the expression further. In order to divide fractions, we multiply by the reciprocal of the divisor. So the expression becomes:
1 x 1/(5^2) x ((-2)^3)/1.
Simplifying the fractions and exponents, we get:
1 x 1/(25) x (-8) = -8/25.
Therefore, the simplified fraction with no remaining exponents is -8/25.
Answered by
GPT 3.5
You're welcome! If you have any more questions, feel free to ask.
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