which expression is correctly developed to use the power rule of exponents? (7^4)^8, (7^8) x (7^10), 12^9, (-5)^0
The expression that is correctly developed to use the power rule of exponents is (7^8) x (7^10).
To use the power rule of exponents, we apply the rule that states: (a^m)^n = a^(m*n).
Let's apply this rule to each expression:
1. (7^4)^8:
By applying the power rule, we multiply the exponents: 4 * 8 = 32.
Therefore, (7^4)^8 is correctly developed as 7^32.
2. (7^8) x (7^10):
The power rule is not applied to this expression. Rather, when multiplying two expressions with the same base, we add the exponents: 8 + 10 = 18.
Therefore, (7^8) x (7^10) is correctly developed as 7^18.
3. 12^9:
No power rule is needed for this expression. The expression is already in its simplest form.
Therefore, 12^9 is correctly developed as 12^9.
4. (-5)^0:
The power rule states that any non-zero number raised to the power of 0 is equal to 1.
Therefore, (-5)^0 is correctly developed as 1.
To use the power rule of exponents, we need to remember that when we raise a power to another exponent, we multiply the exponents together.
Let's break down each expression to see which one correctly uses the power rule of exponents:
1. (7^4)^8: To solve this expression using the power rule, we multiply the exponents, so 4 * 8 = 32. Therefore, the correct expression is (7^4)^8.
2. (7^8) x (7^10): In this expression, we are multiplying two terms with the same base, which means we can use the power rule of exponents and add the exponents together. So, 8 + 10 = 18. Thus, the correct expression is (7^8) x (7^10).
3. 12^9: This expression does not involve the power rule because there is no exponent applied to another exponent. It is simply multiplying the base 12 by itself 9 times.
4. (-5)^0: According to the power rule, any nonzero number raised to the power of zero is equal to 1. Thus, the correct expression is (-5)^0.
So, from the given options, the expressions that correctly use the power rule of exponents are (7^4)^8 and (-5)^0.