SAT Math Problems | Summary and Q&A

TL;DR

Rewriting expressions with common bases and applying exponent properties to solve exponential equations.

Key Insights

• 😑 Rewriting expressions with common bases simplifies exponential equations.
• 🤨 Exponents can be multiplied when raising one exponent to another.
• ⚾ When dividing exponents with a common base, the exponents are subtracted.
• 🆘 Replacing given values in equations can help solve for unknown variables.
• ❓ Practice and familiarity with exponent properties can assist in solving similar problems efficiently.
• 😑 Utilizing calculators can aid in finding the actual values of expressions if allowed.
• ⌛ Checking possible solutions by plugging in values can save time in time-constrained tests.

Transcript

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Questions & Answers

Q: How can you solve an equation with exponential expressions?

To solve an equation with exponential expressions, rewrite the expressions with a common base and apply exponent properties such as multiplication and division of exponents.

Q: What is the process for rewriting expressions with common bases?

The process involves identifying the common base of the given expressions and replacing them accordingly. In this case, 81 is replaced with 3 to the fourth power (3^4) and 27 is replaced with 3 to the third power (3^3).

Q: What happens when you raise one exponent to another exponent?

When you raise one exponent to another exponent, it is equivalent to multiplying the two exponents together. In the given example, 4y - 3x becomes 3^(4y - 3x).

Q: How do you simplify an expression with exponents that have a common base?

When dividing two exponents with a common base, you subtract the exponents. In this case, 3^(4y - 3x) becomes 3^(4y - 3x) = 3^(4y) / 3^(3x).

Summary & Key Takeaways

• To solve an equation with exponential expressions, rewrite the expressions with common bases and apply exponent properties.

• Replace the given expressions (81 and 27) with their common base of 3. Multiply the exponents (4y and 3x) to simplify the expression.

• Divide the exponents (4y - 3x) to find the simplified form of the expression. Replace the given value of 4y - 3x with 2.

• Simplify the equation to find the value of the expression as 9. Therefore, Option B is the correct answer.