Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅3^−9 with only positive exponents

Answer 1

To generate an equivalent expression with only positive exponents, we can use the property of exponents that states a^(m+n) = a^m * a^n.

So, let's apply this property to simplify the expression 3^7 * 3^(-9):

We'll rewrite 3^(-9) as 1/3^9, since any number raised to the power of -n is equivalent to 1 divided by that number raised to the power of n.

Therefore, 3^7 * 3^(-9) can be written as 3^7 * (1/3^9).

Now, we can use the property of exponents a^(-n) = 1/a^n, to rewrite the expression as:

3^7 * 1/3^9 = 3^7/3^9

Finally, using the property of exponents a^m/a^n = a^(m-n), we simplify further:

3^7/3^9 = 3^(7-9) = 3^(-2)

Therefore, an equivalent expression to 3^7 * 3^(-9) with only positive exponents is 3^(-2).

Answer 2

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

Answer 3

To generate an equivalent expression with only positive exponents, we multiply the base numbers and add the exponents.

Given expression: 3^7 * 3^(-9)

We add the exponents: 7 + (-9) = -2

Therefore, an equivalent expression to 3^7 * 3^(-9) with only positive exponents is 3^(-2).

To simplify 3^(-2), we use the property a^(-n) = 1/a^n:

1 / 3^2

Simplifying further:

1 / 9

Therefore, the simplified equivalent expression to 3^7 * 3^(-9) with no remaining exponents is 1/9.

Answer 4

Apply the Properties of Integer Exponents to generate equivalent expressions to 2^2/2^−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.

Answer 5

To generate an equivalent expression with only positive exponents, we can use the property of exponents that states a^(-n) = 1/a^n.

Given expression: 2^2/2^(-4)

Using the property above, we can rewrite 2^(-4) as 1/2^4.

Therefore, the expression becomes:

2^2 / (1/2^4)

Next, we can simplify the division by multiplying the numerator by the reciprocal of the denominator:

2^2 * (2^4/1)

Applying the property a^(m+n) = a^m * a^n, we can add the exponents:

2^(2+4)

Simplifying the exponent:

2^6

Therefore, the equivalent expression with only positive exponents is 2^6.

Solving this expression:

2^6 = 2 * 2 * 2 * 2 * 2 * 2

Simplifying further:

2^6 = 64

Thus, the solution to the expression 2^2/2^(-4) is 64.

Answer 6

Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 5^−2(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answer 7

To generate an equivalent expression with only positive exponents, we'll use the property of exponents that states a^(-n) = 1/a^n.

Given expression: 4^0 * 5^(-2)(-2)^(-3)

Let's simplify each part of the expression separately.

1) 4^0:
Any number raised to the power of 0 is equal to 1. So, 4^0 = 1.

2) 5^(-2):
Using the property a^(-n) = 1/a^n, we can rewrite 5^(-2) as 1/5^2.

3) (-2)^(-3):
Using the property a^(-n) = 1/a^n, we can rewrite (-2)^(-3) as 1/(-2)^3.

Now, we can substitute these simplified terms back into the original expression:

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

Next, we can simplify exponents:

1 * 1/25 * 1/(-8)

Simplifying further:

1/25 * -1/8

Multiplying the numerators: 1 * -1 = -1

Simplifying the denominators: 25 divided by 8 = 25/8

Therefore, the solution to the expression 4^0 * 5^(-2)(-2)^(-3) is -1/25/8, which is equivalent to -1/25 * 8/1.

Multiplying the numerator and denominator:

-1 * 8 = -8

25 * 1 = 25

So, the solution is -8/25.

Answer 8

Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 5^−2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answer 9

To generate an equivalent expression with only positive exponents, we'll use the property of exponents that states a^(-n) = 1/a^n.

Given expression: 4^0 * 5^(-2)/(−2)^(-3)

Let's simplify each part of the expression separately.

1) 4^0:
Any number raised to the power of 0 is equal to 1. So, 4^0 = 1.

2) 5^(-2):
Using the property a^(-n) = 1/a^n, we can rewrite 5^(-2) as 1/5^2.

3) (-2)^(-3):
Using the property a^(-n) = 1/a^n, we can rewrite (-2)^(-3) as 1/(-2)^3.

Now, we can substitute these simplified terms back into the original expression:

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

Next, we can simplify exponents:

1 * 1/25 / 1/(-8)

To divide fractions, we multiply the first fraction by the reciprocal of the second:

1 * 1/25 * (-8)/1

Simplifying:

-8/25

Therefore, the solution to the expression 4^0 * 5^(-2)/(−2)^(-3) is -8/25.

Answer 10

Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Answer 11

Let's apply the properties of integer exponents to simplify the expression (14^3⋅27^−7)^0/3^4 and obtain an equivalent expression with only positive exponents.

First, we can rewrite 27^(-7) as 1/27^7, since 27^(-n) is equivalent to 1 divided by 27^n.

The expression becomes (14^3⋅(1/27^7))^0/3^4.

Using the exponent property (a^m)^n = a^(m*n), we can multiply the exponents inside the parentheses:

(14^3 * 1/27^7)^0/3^4.

Simplifying further, we have:

(14^3/27^7)^0/3^4.

Now, we apply the property (a/b)^n = a^n/b^n:

14^(3*0)/27^(7*0)/3^4.

Since any number raised to the power of 0 is equal to 1, both 14^(3*0) and 27^(7*0) will become 1:

1/1/3^4.

To divide fractions, we multiply the first fraction by the reciprocal of the second:

1 * 3^4/1.

Thus, the expression (14^3⋅27^−7)^0/3^4 simplifies to 3^4.

Evaluating 3^4, we have:

3^4 = 3 * 3 * 3 * 3 = 81.

Therefore, the solution to the expression is 81.