Math Problem Statement

can you solve these problems?

can you solve these problems?

Solution

Yes, I can help you solve these problems!

Let's break them down:

Problem 1:

The expression is:

(u7v)(9v4)(u^7 v)(9v^4)

Solution:

  1. Apply the multiplication rule for exponents. The variables with the same base should have their exponents added. Here, we have vv in both terms: u7v9v4u^7 \cdot v \cdot 9 \cdot v^4
  2. Combine the terms: u79v1+4u^7 \cdot 9 \cdot v^{1 + 4} which simplifies to: 9u7v59u^7v^5

So, the simplified expression is: 9u7v59u^7v^5


Problem 2:

The expression is:

9(v4)2-9(v^4)^2

Solution:

  1. Apply the power of a power rule, which states that when you raise a power to another power, you multiply the exponents: (v4)2=v4×2=v8(v^4)^2 = v^{4 \times 2} = v^8
  2. Now multiply by 9-9: 9v8-9v^8

So, the simplified expression is: 9v8-9v^8


Would you like any more details on these solutions or have any further questions?

Here are 5 related questions for practice:

  1. How do you simplify (x3)(4x5)(x^3)(4x^5)?
  2. Simplify (2y3)(5y6)(-2y^3)(5y^6).
  3. Simplify (3a2b4)(2ab3)(3a^2b^4)(2ab^3).
  4. How do you simplify (5x2y3)2(5x^2y^3)^2?
  5. Simplify 4(z5)3-4(z^5)^3.

Tip: When multiplying variables with the same base, always add their exponents!

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra
Multiplication of Terms

Formulas

Power of a Power Rule: (x^a)^b = x^(a*b)
Multiplication Rule for Exponents: x^a * x^b = x^(a+b)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10