https://file.aiquickdraw.com/mathbot/file/1727884066084h53ljfx0.jpg

The image contains the following set of expressions to be simplified:

**Task: "Suprastinkite reiškinį" translates to "Simplify the expression."**

1. \( (2x)^3 \)
2. \( (4y)^2 \)
3. \( (4x^2)^3 \)
4. \( (6y^5)^2 \)
5. \( (-2x)^4 \)
6. \( (-3y)^3 \)
7. \( \left(\frac{2x^3}{y}\right)^3 \)
8. \( \left(\frac{2x^2}{y}\right)^6 \)

Let’s simplify each one step-by-step:

### a) \( (2x)^3 \)
\[
(2x)^3 = 2^3 \cdot x^3 = 8x^3
\]

### b) \( (4y)^2 \)
\[
(4y)^2 = 4^2 \cdot y^2 = 16y^2
\]

### c) \( (4x^2)^3 \)
\[
(4x^2)^3 = 4^3 \cdot (x^2)^3 = 64x^6
\]

### d) \( (6y^5)^2 \)
\[
(6y^5)^2 = 6^2 \cdot (y^5)^2 = 36y^{10}
\]

### e) \( (-2x)^4 \)
\[
(-2x)^4 = (-2)^4 \cdot x^4 = 16x^4
\]

### f) \( (-3y)^3 \)
\[
(-3y)^3 = (-3)^3 \cdot y^3 = -27y^3
\]

### g) \( \left( \frac{2x^3}{y} \right)^3 \)
\[
\left( \frac{2x^3}{y} \right)^3 = \frac{2^3 \cdot (x^3)^3}{y^3} = \frac{8x^9}{y^3}
\]

### h) \( \left( \frac{2x^2}{y} \right)^6 \)
\[
\left( \frac{2x^2}{y} \right)^6 = \frac{2^6 \cdot (x^2)^6}{y^6} = \frac{64x^{12}}{y^6}
\]

### Final Simplified Results:
a) \( 8x^3 \)  
b) \( 16y^2 \)  
c) \( 64x^6 \)  
d) \( 36y^{10} \)  
e) \( 16x^4 \)  
f) \( -27y^3 \)  
g) \( \frac{8x^9}{y^3} \)  
h) \( \frac{64x^{12}}{y^6} \)

Would you like more details or have any questions?

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**Related Questions:**

1. How do you apply the power of a product rule in exponentiation?
2. What happens when you raise a negative number to an even power versus an odd power?
3. How can you simplify fractions with exponents?
4. How do you handle exponents in expressions with multiple variables?
5. Can you explain how to deal with negative exponents?

**Tip:** Always apply the exponent to both the coefficient and the variable when simplifying expressions.

Simplify the following expressions: (2x)^3, (4y)^2, (4x^2)^3, (6y^5)^2, (-2x)^4, (-3y)^3, (2x^3/y)^3, (2x^2/y)^6.

This page explains how to simplify algebraic expressions such as (2x)^3, (4y)^2, (4x^2)^3, (6y^5)^2, (-2x)^4, (-3y)^3, (2x^3/y)^3, and (2x^2/y)^6. Suitable for students in Grades 7-9, it covers exponentiation rules including powers of variables, power of a product, and more.

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