Exponent Rules Unit Test
Use the product rule of exponents to simplify 5^10 * 5^5
responses
a. 5^15
b. 25^15
c. 25^50
d. 5^50
To find the numerical equivalent of 9^3, we need to evaluate the expression.
9^3 means multiplying 9 by itself three times.
9^3 = 9 * 9 * 9 = 729
So, the numerical equivalent of 9^3 is 729.
2^0 is equal to 1, so the expression 6.9 - 2^0 becomes 6.9 - 1.
6.9 - 1 = 5.9.
Therefore, the value of 6.9 - 2^0 is 5.9.
So the correct answer is: d. 5.9
To create an equivalent expression for the problem:
9 * (-33)^0 + 3/2 * (8 - 27^0)
Using the zero power rule, we know that any non-zero number raised to the power of 0 equals 1. Therefore, (-33)^0 is equal to 1.
So, the expression becomes:
9 * 1 + 3/2 * (8 - 1)
Simplifying further:
9 + 3/2 * 7
To multiply a fraction by a whole number, we can multiply the numerator by the whole number:
9 + (3 * 7) / 2
9 + 21/2
To add fractions with a common denominator, we add the numerators:
(18/2 + 21/2) / 2
39/2 / 2
To divide a fraction by a whole number, we multiply the numerator by the reciprocal of the whole number:
39/2 * 1/2
39/4
So, an equivalent expression for the problem is:
9 * (-33)^0 + 3/2 * (8 - 27^0) = 39/4
The product rule of integer exponents states that when multiplying two numbers with the same base, you add their exponents.
To find the numerical equivalent of 12^-5 * 12^7, we can apply the product rule and add the exponents:
12^-5 * 12^7 = 12^(-5 + 7)
Simplifying the exponent, -5 + 7 = 2.
Therefore, 12^-5 * 12^7 simplifies to 12^2.
To find the numerical value, we can calculate 12^2:
12^2 = 144.
So, the numerical equivalent of 12^-5 * 12^7 is 144.
The product rule of exponents states that when multiplying two numbers with the same base, you add their exponents.
Therefore, 5^10 * 5^5 would simplify to 5^(10+5), which is equivalent to 5^15.
So the correct answer is: a. 5^15
Find the numerical equivalent of 9^9 * 9^-6
When multiplying two numbers with the same base but different exponents, you subtract the exponent of the second number from the exponent of the first number.
Therefore, 9^9 * 9^-6 would simplify to 9^(9 - 6), which is equivalent to 9^3.
So the numerical equivalent of 9^9 * 9^-6 is 9^3.
Find the numerical equivalent of 9^3
what is the missing exponent in the following equation?
h^420/h^? = h^215
To find the missing exponent in the equation h^420/h^? = h^215, we can use the quotient rule of exponents.
According to the quotient rule of exponents, when dividing two numbers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.
Therefore, h^420/h^? is equal to h^(420 - ?).
The equation h^420/h^? = h^215 can be written as h^(420 - ?) = h^215.
To match the exponents on both sides of the equation, we set the exponents equal to each other:
420 - ? = 215
Now, we solve for ?:
420 - 215 = ?
205 = ?
Therefore, the missing exponent in the equation is 205.