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 1

Using the properties of integer exponents, we can rewrite 2^2 / 2^-4 as follows:

2^2 / 2^-4 = 2^(2 + 4)

Now, let's simplify the expression:

2^(2 + 4) = 2^6

Since 2^6 means multiplying 2 by itself six times, we can calculate the value as:

2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64

Therefore, the solution to the expression 2^2 / 2^-4 is 64.

Answer 2

thanks bot!

Answer 3

You're welcome! If you have any more questions, feel free to ask. I'm here to help!

Answer 4

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.

Answer 5

To simplify the expression 4^0 x 5^-2 / (-2)^-3 using properties of integer exponents, we can make use of the rule that any number raised to the power of zero is equal to 1. Also, negative exponents can be rewritten as the reciprocal of the positive exponent.

Let's rewrite the expression step by step:

4^0 x 5^-2 / (-2)^-3

Since 4^0 = 1, we have:

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

Now, let's rewrite the negative exponents as reciprocals:

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

Simplifying further:

1 x (1/25) / (1/(-8))

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

1 x (1/25) x (-8/1)

Simplifying the product:

(-8/25)

Therefore, the simplified fraction equivalent to the expression 4^0 x 5^-2 / (-2)^-3 is -8/25.

Answer 6

Apply the properties of integer exponents to generate equivalent expressions to (14^3 x 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 7

To generate equivalent expressions and solve the given expression, we'll follow these steps using the properties of integer exponents:

Step 1: Distribute the exponent outside the parentheses:

(14^3 x 27^-7)^(0/3^4)

Step 2: Simplify the exponent of 27 by applying the rule that says a negative exponent can be rewritten as the reciprocal with a positive exponent:

(14^3 x (1/27^7))^(0/3^4)

Step 3: Simplify the denominator by evaluating 0/3^4, which is equal to 0:

(14^3 x (1/27^7))^0

Step 4: Apply the rule that any expression raised to the power of zero is equal to 1:

1

Therefore, the solution to the expression (14^3 x 27^-7)^0/3^4 is 1.

Answer 8

wrong, sorry

Answer 9

Apologies for the mistake. Let's approach the problem again:

To generate equivalent expressions and solve the expression (14^3 x 27^-7)^(0/3^4), we can follow these steps using the properties of integer exponents:

Step 1: Simplify the exponents inside the parentheses:

(14^3 x (1/27^7))^0/3^4

Step 2: Simplify the numerator and denominator separately:

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

Step 3: Since anything raised to the power of zero is equal to 1, we can simplify further:

1/3^4

Step 4: Simplify the exponent of 3:

1/81

Therefore, the solution to the expression (14^3 x 27^-7)^(0/3^4) is 1/81.

Answer 10

Apply the properties of integer exponents to generate equivalent expressions to (4^3 x 7^-2)^-5/7^9 x 4^13 with only positive exponents, then solve the expression. your answer will be a simplified fraction with no remaining exponents.

Answer 11

To generate equivalent expressions and solve the given expression, we'll follow these steps using the properties of integer exponents:

Step 1: Apply the power rule to simplify the exponents inside the parentheses:

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

Step 2: Simplify the negative exponent by rewriting it as the reciprocal with a positive exponent:

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

Step 3: Simplify the fraction exponent by applying the power rule for exponents:

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

Step 4: Apply the power rule to simplify the exponent of 4:

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

Step 5: Multiply the exponents inside the parentheses:

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

Step 6: Simplify the exponents of 4 and 7:

(64^(5/7^9) x ((1/49)^(-5/7^9))) x 4^13

Step 7: Simplify the bases by evaluating the powers of 64 and 49:

((1/536870912 x (49^5))^(-1/35831808)) x 4^13

Step 8: Simplify the fraction exponent of 49:

((1/536870912 x (49^5))^(-1/35831808)) x 4^13

Step 9: Simplify the bases by evaluating the powers of 49 and 4:

((1/536870912 x 5764801)^(-1/35831808)) x 67108864

Step 10: Simplify the exponent by applying the power rule:

(1/536870912 x 5764801)^(1/35831808) x 67108864

Step 11: Perform the operation inside the parentheses:

(5764801/536870912)^(1/35831808) x 67108864

Step 12: Simplify the fraction exponent by applying the power rule:

(5764801/536870912)^(1/35831808) x 67108864

Therefore, the final solution is given by (5764801/536870912)^(1/35831808) multiplied by 67108864.