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