Simplifying Exponents - Algebra II

Card 0 of 1232

Question

Simplify $x^5y^2x^{-4}$

Answer

First, combine exponents of like variables. This gives us

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Question

Simplify $z^3y^2x^6y^{-3}$

Answer

First, combine exponents of like variables. This gives us $z^3y^{-1}x^6$ which simplifies to $\frac{z^3x^6}{y}$

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Question

Simplify.

$3^{-14}3^{23}3^{-15}$

Answer

When multiplying exponents with the same base, you just have to add the exponents.

$3^{-14}3^{23}3^{-15}=3^{-14+23-15}=3^{-6}$

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Question

Simplify.

$\frac{a^{45}}{a^{30}}$

Answer

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{45}}{a^{30}}=a^{45-30}=a^{15}$

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Question

Simplify.

$\frac{a^7}{a^{18}}$

Answer

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{7}}{a^{18}}=a^{7-18}=a^{-11}$

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Question

Simplify: $12^{19}\div12^7$

Answer

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

$12^{19}\div12^7=12^{19-7}=12^{12}$

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Question

Simplify:

Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$23^7*23^8=23^{7+8}=23^{15}$

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Question

Simplify: $2^4*2^{-12}$

Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$2^4*2^{-12}=2^{4+(-12)}=2^{-8}$

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Question

Simplify: $(-3)^7*(-3)^{-2}$

Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$(-3)^7*(-3)^{-2}=(-3)^{7+(-2)}=(-3)^{5}$

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Question

Simplify:

Answer

When multiplying exponents with the same base, we just keep the base the same and add the exponents.

$x^5*x^6=x^{5+6}=x^{11}$

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Question

Simplify: $x^{12}*x^{-8}$

Answer

When multiplying exponents with the same base, we just keep the base the same and add the exponents.

$x^{12}*x^{-8}=x^{12+(-8)}=x^4$

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Question

Simplify:

$(5^{-8})^{-12}$

Answer

When dealing with exponents being raised by another exponent, we just multiply the powers and keep the base the same.

$(5^{-8})^{-12}=5^{-8*-12}=5^{96}$

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Question

Simplify: $(3a^2b^{-3}c^4)^2$

Answer

To simplify this expression, square every term in the parentheses:

$3^2a^4b^{-6}c^8$ .

Then simplify and get rid of the negative exponent by putting the b term on the denominator:

$\frac{9a^4c^8}{b^6}$ .

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Question

Simplify:

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(4^7)^7=4^{7*7}=4^{49}$

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Question

Simplify:

$(8^7)^{-2}$

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(8^7)^{-2}=8^{7*-2}=8^{-14}$

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Question

Simplify:

$(5^{-5})^{-5}$

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(5^{-5})^{-5}=5^{-5*-5}=5^{25}$

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Question

What is the largest positive integer, , such that is a factor of ?

Answer

. Thus, is equal to 16.

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Question

Solve:

Answer

Solve each term separately. A number to the zeroth power is equal to 1, but be careful to apply the signs after the terms have been simplified.

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Question

Evaluate:

Answer

When dealing exponents being raised by a power, we multiply the exponents and keep the base.

$(2^9)^4=2^{9*4}=2^{36}$

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Question

Evaluate:

$(5^{6})^7$

Answer

When dealing exponents being raised by a power, we multiply the exponents and keep the base.

$(5^{6})^7=5^{6*7}=5^{42}$

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