About Negative Exponents:
In order to be successful with polynomials, we must have a great understanding of exponents. We previously learned about the product rule for exponents, along with the power rules. In this lesson, our focus was on the quotient rule for exponents. Additionally, we learned how to simplify negative exponents and work with an exponent of zero.
Test Objectives
- Demonstrate the ability to simplify exponential expressions using the product rule for exponents
- Demonstrate the ability to simplify exponential expressions using the quotient rule for exponents
- Demonstrate the ability to simplify exponential expressions using the power rules for exponents
- Demonstrate the ability to simplify exponential expressions with negative exponents
- Demonstrate the ability to simplify exponential expressions with an exponent of zero
#1:
Instructions: Simplify by writing with positive exponents. Assume that all variables represent nonzero real numbers.
a) $$(2x^5y^3)^{-4} \cdot -2y^2$$
b) $$(2m^3n^{-4})^{-3} \cdot -2m^5n^0$$
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#2:
Instructions: Simplify by writing with positive exponents. Assume that all variables represent nonzero real numbers.
a) $$2x^2 \cdot (2x^3y^{-1})^{-3}$$
b) $$\left[\frac{(-2n^{-4})^2 \cdot (n^{-4})^5}{-n^3}\right]^4$$
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#3:
Instructions: Simplify by writing with positive exponents. Assume that all variables represent nonzero real numbers.
a) $$-\frac{pqm^2 \cdot pq}{(2mp^2q^2)^2}$$
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#4:
Instructions: Simplify by writing with positive exponents. Assume that all variables represent nonzero real numbers.
a) $$\frac{(2pn^{-1})^{-2} \cdot -2pm^2n^{-2}}{m^2n^2}$$
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#5:
Instructions: Simplify by writing with positive exponents. Assume that all variables represent nonzero real numbers.
a) $$\frac{2np^2 \cdot mn^0p^2(-2pm^{-1}n^2)^{-1}}{-2pm^2n^{-2}}$$
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Written Solutions:
#1:
Solutions:
a) $$-\frac{1}{8x^{20}y^{10}}$$
b) $$-\frac{n^{12}}{4m^{4}}$$
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#2:
Solutions:
a) $$\frac{y^3}{4x^7}$$
b) $$\frac{256}{n^{124}}$$
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#3:
Solutions:
a) $$-\frac{1}{4p^2q^2}$$
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#4:
Solutions:
a) $$-\frac{1}{2pn^2}$$
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#5:
Solutions:
a) $$\frac{p^2n}{2}$$
