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Zorluk: KolayOperations with Variable Exponents

Match each algebraic expression containing numerical coefficients on the left with its fully simplified equivalent form on the right.

  • 3y2⋅2y43y^2 \cdot 2y^46y66y^6
  • 12y74y3\frac{12y^7}{4y^3}3y43y^4
  • (2y3)3(2y^3)^38y98y^9
  • 5y−25y^{-2}5y2\frac{5}{y^2}

Cevap

The simplified pairs are: 3y2⋅2y43y^2 \cdot 2y^4 matches with 6y66y^6, 12y74y3\frac{12y^7}{4y^3} matches with 3y43y^4, (2y3)3(2y^3)^3 matches with 8y98y^9, and 5y−25y^{-2} matches with 5y2\frac{5}{y^2}.
Each left-side expression simplifies to exactly one unique form on the right by appropriately applying exponent rules to the variable bases and standard arithmetic operations to the numerical coefficients.

Adım Adım Çözüm

1
Simplify the product expression 3y2⋅2y43y^2 \cdot 2y^4.
6y66y^6
When multiplying terms, handle coefficients and variables separately. Multiply coefficients (3×2=63 \times 2 = 6) and add exponents for identical bases (y2+4=y6y^{2+4} = y^6).
2
Simplify the quotient expression 12y74y3\frac{12y^7}{4y^3}.
3y43y^4
Divide the coefficients (12÷4=312 \div 4 = 3) and subtract the bottom exponent from the top exponent (y7−3=y4y^{7-3} = y^4).
3
Simplify the power expression (2y3)3(2y^3)^3.
8y98y^9
Raise both the coefficient and the variable to the power of 3. Calculate 23=82^3 = 8, and multiply the exponents for the variable 3×3=93 \times 3 = 9.
4
Simplify the negative exponent expression 5y−25y^{-2}.
5y2\frac{5}{y^2}
A negative exponent creates a reciprocal. Since the exponent only applies to yy, it moves to the denominator while the coefficient 5 stays in the numerator.

Anahtar Kavram

Handling numerical coefficients alongside basic operations with variable exponents.
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Konular

Operations with Variable Exponents

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