Laws of exponents

Laws of exponents

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Multiple Choice

According to exponent rules, when we multiply expressions with the same base we _______ the exponents.

• Multiply

• Add

• Divide

• Subtract

Multiple Choice

According to exponent rules, when we divide expressions with the same base we _______ the exponents.

• Multiply

• Add

• Divide

• Subtract

Multiple Choice

According to exponent rules, when we raise the power to a power we _______ the exponents.

• add

• subtract

• multiply

• divide

Multiple Choice

A number raised to a zero exponent is always ________

• 0

• 1

• undefined

Multiple Choice

When a number has no exponent , its exponent is understood to be ______.

• 1

• 0

• 10

Multiple Choice

A number raised to the exponent 1 is equal to the ________ itself.

• 1

• 0

• number

• 100

Multiple Choice

 $\left(\frac{2}{3}\right)^3\ =$  

•  $\frac{8}{27}$  

•  $\frac{6}{9}$  

•  $\frac{2}{3}$  

•  $\frac{2}{9}$  

Multiple Choice

Anything raised to a power of zero is always:

• 0

• 1

• itself

• negative

Multiple Choice

 $5^{-3}\ should\ be\ simplified\ to:$  

•  $\frac{1}{5^3}$  

•  $5^{\frac{1}{3}}$  

•  $3^{\frac{1}{5}}$  

•  $\frac{3}{5^{-1}}$  

Multiple Choice

(5³x²y⁴)⁰

• 5xy

• 1

• 0

• 5

Multiple Choice

How do you write

5⋅5⋅5⋅5⋅5⋅5⋅5

with an exponent?

• 5⁷

• 5⁶

• 7⁵

• 5

Multiple Choice

Simplify:

(x³)(x²)

• x⁵

• x⁶

• x

• x^1.5

Multiple Choice

(6x²)(-3x⁵)

• 18x⁷

• -18x⁷

• 18x¹⁰

• 3x⁷

Multiple Choice

Simplify (-4r⁵)(2r⁸)

• -8r¹³

• -2r¹³

• -8r⁴⁰

• -2y⁴⁰

Multiple Choice

Simplify:

(3t²)³

• 9t⁶

• 9t⁵

• 27t⁶

• 27t⁵

Multiple Choice

Simplify: (2ab)³

• 2³a³b³

• 2ab³

• 6a³b³

• 6ab

Multiple Choice

Simplify the following expression:
 $\frac{30y^{12}}{15y^2}$  

• 2y²⁴

• 2¹⁰

• 2y¹⁰

• 2y¹⁴

Multiple Choice

Which expression is equivalent to the given?

Multiple Choice

Replace  $a$ and  $b$   so that the following equation is equivalent to $x^6$ .

 $\left(\frac{1}{x^a}\right)^b$  

•  $a=4;\ b=2$  

•  $a=-3;\ b=2$  

•  $a=-2;\ b=-3$  

•  $a=1;\ b=6$  

Multiple Choice

Make this negative exponent positive.

9^-3

• 9³

• $\frac{1}{9^{-3}}$

• $\frac{1}{9^3}$

• 729

Multiple Choice

Simplify the following expression:

 $\frac{x^{18}y^{15}}{x^6y^3}$  

• x³y⁵

• x¹²y¹²

• x²⁴y¹⁸

• x¹⁰⁸y⁴⁵

Multiple Choice

Evaluate the expression using the quotient rule.

• 3⁴

• $\frac{1}{3^4}$

• 3^-12

• 3³²

Multiple Choice

Simplify the following expression:

xy^-7

• xy⁷

• x/y⁷

• x⁷/y

• x⁷y

Multiple Choice

Simplify the exponential expression.

• 2x⁶y¹²
• 2x⁵y⁷
• 8x⁶y¹²
• 8x⁵y⁷

Multiple Choice

Evaluate the expression using the quotient rule.

• 2¹⁴ z¹³

• 2²/z⁷

• 2¹⁴/ z⁷

• 2² z⁷

Multiple Choice

 $\left(\frac{3}{4}\right)^2\ =\ ?$  

•  $\frac{9}{4}$  

•  $\frac{6}{8}$  

•  $\frac{9}{16}$  

•  $\frac{6}{4}$  

Multiple Choice

True or false
 $\left(\frac{x}{y}\right)^3\ =\ \frac{3x}{3y}$  

• True

• False

Multiple Choice

 $64^{\frac{1}{2}}$  

•  $\sqrt{64\ }\ =\ 8$  

•  $\sqrt{64^2\ }\ =\ 64$  

•  $\sqrt{64^{\frac{1}{2}}}\ =\ \sqrt{8}$  

•  $\sqrt{32}$  

Multiple Choice

 $100^{\frac{3}{2\ }}\ \ can\ be\ simplified\ to\ \sqrt{100^3}=1000$  

True or False

• True

• False

Poll

I can multiply correctly expressions with the same bases.

• with great confidence

• with moderate confidence

• I am still confused

Poll

I can divide correctly expressions with the same bases.

• with great confidence

• with moderate confidence

• I am still confused

Poll

I can raise a power to another power correctly.

• with great confidence

• with moderate confidence

• I am still confused

Poll

I know the following:

Any number raised to the zero power is always 1

A number raised to 1 is always the same number.

A negative exponent can be made positive by changing its position in the other side of the fraction bar.

• I can remember that easy

• It is pretty hard to remember.

• I can't put it in my head, but I have to. I will try.

Poll

I will always remember that a number with a rational exponent can be changed to radical by making the denominator of the exponent as the index of the radical and the numerator as the exponent under the radical.

• Yes, I can and will remember that.

• I'm still confused. I need more examples.