Simplify using Exponent Rules: 7^4×7×7^13×7^−20
(1 point)
Using the exponent rules, we know that when multiplying variables with the same base, we add the exponents.
Applying this rule, we can simplify the expression as follows:
7^4 × 7 × 7^13 × 7^(-20)
= 7^(4 + 1 + 13 + (-20))
= 7^(-2)
Therefore, the simplified expression is 7^(-2).
Simplify using Exponent Rules: 7^4×7×7^13×7^−20
(1 point)
28^−2
28 to the negative 2 power
1/7^2
the fraction with numerator 1 and denominator 7 squared
1/7^3
the fraction with numerator 1 and denominator 7 cubed
1/7^−2
To simplify the expression 7^4 × 7 × 7^13 × 7^(-20), we add the exponents when multiplying variables with the same base.
Therefore,
7^4 × 7 × 7^13 × 7^(-20) = 7^(4 + 1 + 13 + (-20))
Simplifying inside the parentheses, we have:
7^(4 + 1 + 13 + (-20)) = 7^(-2)
So, the simplified expression is 7^(-2).
Note: The answer choices provided do not match the given expression.
Fully simplify using Exponent Rules:(5^8/5^6)^2
(1 point)
A. 1^4
B. 5^2
C. 25^4
D. 5^4
To simplify (5^8/5^6)^2 using exponent rules, we can first simplify the expression inside the parentheses by subtracting the exponents:
(5^8/5^6)^2 = 5^(8-6)^2
Simplifying inside the parentheses:
= 5^2^2
Then, using the exponent rule for raising a power to another power, we multiply the exponents:
= 5^(2*2)
= 5^4
Therefore, the fully simplified expression is 5^4. The answer is D. 5^4.
To simplify the expression using exponent rules, we can apply the rule that states when multiplying two numbers with the same base, we add their exponents.
First, let's simplify the exponents:
7^4 × 7 × 7^13 × 7^(-20)
To multiply 7^4 and 7^13, we add their exponents:
7^(4+13) × 7 × 7^(-20)
Now, let's simplify the exponent (4+13):
7^17 × 7 × 7^(-20)
Next, we multiply 7^17 and 7:
7^(17+1) × 7^(-20)
Simplifying the exponent (17+1):
7^18 × 7^(-20)
Finally, to multiply 7^18 and 7^(-20), we add their exponents:
7^(18+(-20))
Simplifying the exponent (18+(-20)):
7^(-2)
Therefore, the simplified expression is 7^(-2).
To simplify the expression using exponent rules, we can apply the rule that states:
a^m × a^n = a^(m + n)
Let's simplify step by step:
The expression is: 7^4 × 7 × 7^13 × 7^(-20)
First, we can combine the 7^4 and 7^13 terms:
7^4 × 7^13 = 7^(4 + 13) = 7^17
Now, we have 7 × 7^(-20) left. According to the same rule, we can combine these terms as well:
7 × 7^(-20) = 7^(1 + (-20)) = 7^(-19)
So, our expression is now simplified to:
7^17 × 7^(-19)
Using another exponent rule that states:
a^m × a^n = a^(m - n)
We can simplify further:
7^17 × 7^(-19) = 7^(17 - 19) = 7^(-2)
Therefore, the simplified form of the expression 7^4 × 7 × 7^13 × 7^(-20) is 7^(-2).