Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents

Answer 1

First, let's rewrite the expression 37⋅3−9 using the properties of integer exponents:

37⋅3−9 = 3^7 ⋅ 3^(-9)

According to the property of multiplying powers with the same base, we can add the exponents:

3^7 ⋅ 3^(-9) = 3^(7+(-9))

Now, let's simplify the sum of the exponents:

7+(-9) = -2

Therefore, the expression is equivalent to:

37⋅3−9 = 3^(-2)

To solve the expression, we need to write it as a fraction with positive exponents:

3^(-2) = 1/3^2

Simplifying the fraction:

1/3^2 = 1/9

So the final answer is 1/9.

Answer 2

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Answer 3

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Answer 4

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Answer 5

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Answer 6

apply the Properties of Integer Exponents to generate equivalent expressions to (4^3 ⋅ 7^−2)−5^/7^9 ⋅ 4^−13 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

Answer 7

Let's apply the Properties of Integer Exponents to generate equivalent expressions for the given expression.

(4^3 ⋅ 7^−2)−5^/7^9 ⋅ 4^−13

Using the property of multiplying powers with the same base, we can rewrite (4^3 ⋅ 7^−2) as 4^3 ⋅ 7^−2.

Using the property of dividing powers with the same base, we can rewrite 5^/7^9 as 5^7/7^9.

Therefore, the expression becomes:

(4^3 ⋅ 7^−2)/(5^7/7^9) ⋅ 4^−13

Now let's simplify the expression by applying the rules of exponents:

(4^3 ⋅ 7^−2)/(5^7/7^9) ⋅ 4^−13

Using the rule a^m/n = (n√a)^m:

(4^(3/1) ⋅ 7^(-2/1))/(5^(7/1) ⋅ 7^(9/1)) ⋅ 4^(-13/1)

Simplifying the exponents:

4^3 ⋅ 7^(-2)/(5^7 ⋅ 7^9) ⋅ 4^(-13)

Now, let's combine the like terms using the rule a^m ⋅ a^n = a^(m+n):

(4^3 ⋅ 7^(-2) ⋅ 4^(-13))/(5^7 ⋅ 7^9)

Applying the rule of subtracting exponents in the denominator:

(4^3 ⋅ 7^(-2) ⋅ 4^(-13))/(5^7 ⋅ 7^(9-7))

Simplifying the exponents:

(4^3 ⋅ 7^(-2) ⋅ 4^(-13))/(5^7 ⋅ 7^2)

Since we want to express everything with positive exponents, let's apply the rule a^(-n) = 1/(a^n):

(4^3 ⋅ 1/(7^2) ⋅ 1/(4^13))/(5^7 ⋅ 7^2)

Simplifying the expression:

(4^3)/(7^2 ⋅ 5^7 ⋅ 4^13)

Now, let's combine the powers using the rule a^m ⋅ b^m = (a⋅b)^m:

((4⋅4⋅4)/(7⋅7))/(5^7 ⋅ 4^13)

Simplifying further:

64/(49 ⋅ 4)/(5^7 ⋅ 4^13)

Now, let's express 4 as 2^2:

64/(49 ⋅ 2^2)/(5^7 ⋅ 2^13)

Simplifying:

64/(49 ⋅ 4)/(5^7 ⋅ 2^13)

Now, let's express 49 as 7^2:

64/(7^2 ⋅ 4)/(5^7 ⋅ 2^13)

Simplifying:

64/(7^2 ⋅ 4)/(5^7 ⋅ 2^13)

Now, let's simplify the expression inside the parentheses and combine like terms:

64/(49 ⋅ 4)/(2^13 ⋅ 5^7)

64/(196)/(8192 ⋅ 5^7)

Now, let's simplify further:

64/(196)/(8192 ⋅ 78125)

Now, let's divide 64 by 196:

1/(3)/(8192 ⋅ 78125)

Now, let's multiply 8192 and 78125:

1/(236,421,120)

So, the simplified fraction with no remaining exponents is 1/236,421,120.

Answer 8

Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅3^−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents

Answer 9

Apply the Properties of Integer Exponents to generate equivalent expressions 2^2/2-^4