Exponent Laws and Equivalent Expressions Challenge

This video tutorial covers exponent laws, including the product, quotient, zero, power, expanded power, and negative exponent rules. It explains how to apply these rules with examples and encourages practice. The tutorial also introduces equivalent expressions, demonstrating how to use graphing to identify equivalent polynomials. Students are guided through examples and encouraged to practice using their calculators.

What does the product rule in exponent laws state about the bases?

• Divide the bases and subtract the exponents

• Multiply the bases and add the exponents

• Keep the base the same and add the exponents

• Subtract the exponents and keep the base

According to the quotient rule, what should you do when dividing terms with the same base?

• Divide the exponents

• Subtract the exponents

• Multiply the exponents

• Add the exponents

What is the result of any non-zero number raised to the zero power?

• One

• The base itself

• Zero

• Undefined

In the power rule, how do you handle a power outside the parentheses?

• Multiply it with the powers inside

• Subtract it from the powers inside

• Add it to the powers inside

• Divide it by the powers inside

How does the expanded power rule differ from the basic power rule?

• It involves distributing the outer power to each term inside the parentheses

• It is used exclusively for division problems

• It simplifies expressions without changing the base

• It only applies to numerical bases

When using the power rule, what do you do if you see a power outside the parentheses?

• Multiply the outer power with each exponent inside

• Divide the outer power with each exponent inside

• Add the outer power to each exponent inside

• Ignore the outer power and simplify the inside

What should you do with a term that has a negative exponent?

• Change the sign of the exponent to positive

• Flip the term to the other side of the fraction

• Leave it as is for simplification

• Multiply the base by itself

What is the first step in handling expressions with negative exponents?

• Convert the expression into a polynomial

• Flip the fraction to make the exponent positive

• Subtract the negative exponent from the positive ones

• Multiply the base by the exponent

How can you verify that two expressions are equivalent using a graphing calculator?

• Graph both expressions and check for overlapping curves

• Find the roots of both expressions

• Calculate the derivative of both expressions

• Sum the coefficients of both expressions

In the context of equivalent expressions, what does graphing help to identify?

• The highest degree of the polynomial

• The intercepts on the graph

• Whether two expressions yield the same graph

• The complexity of the expressions