We read your photo as:

Simplify: (cd-c /(d-c) 2 2/(3a)+5/(2b) xcyz2/(abcxyz) Write in standard fo 368 0.00006784 0.00321 458754

Mathematics

ScanSolve AI Answer

Step-by-step solution

15 steps

Here are the solutions to the problems.

4. Simplify:

a) cd−c2(d−c)2\frac{cd-c^2}{(d-c)^2}

  1. Factor out cc from the numerator.

    c(d−c)(d−c)2\frac{c(d-c)}{(d-c)^2}
  2. Cancel one (d−c)(d-c) term from the numerator and denominator.

    cd−c\frac{c}{d-c}

    The simplified expression is cd−c\boxed{\frac{c}{d-c}}.

    b) 23a+52b\frac{2}{3a} + \frac{5}{2b}

  3. Find the least common multiple (LCM) of the denominators $3a$ and $2b$, which is $6ab$.

  4. Rewrite each fraction with the common denominator.

    2⋅(2b)3a⋅(2b)+5⋅(3a)2b⋅(3a)\frac{2 \cdot (2b)}{3a \cdot (2b)} + \frac{5 \cdot (3a)}{2b \cdot (3a)} 4b6ab+15a6ab\frac{4b}{6ab} + \frac{15a}{6ab}
  5. Add the fractions.

    4b+15a6ab\frac{4b+15a}{6ab}

    The simplified expression is 4b+15a6ab\boxed{\frac{4b+15a}{6ab}}.

    c) xcyz2abcxyz\frac{xcyz^2}{abcxyz}

  6. Identify common variables in the numerator and denominator.

    x⋅c⋅y⋅z⋅za⋅b⋅c⋅x⋅y⋅z\frac{x \cdot c \cdot y \cdot z \cdot z}{a \cdot b \cdot c \cdot x \cdot y \cdot z}
  7. Cancel out the common variables (xx, cc, yy, zz).

    zab\frac{z}{ab}

    The simplified expression is zab\boxed{\frac{z}{ab}}.

    5. Write in standard form:

    Standard form (scientific notation) is written as a×10na \times 10^n, where 1≤∣a∣<101 \le |a| < 10 and nn is an integer.

    a) 368

  8. Move the decimal point to the left until there is one non-zero digit before the decimal point.

    3.683.68
  9. Count the number of places the decimal point was moved.

    Since it was moved 2 places to the left, the exponent of 10 is 2.

    3.68×1023.68 \times 10^2

    The standard form is 3.68×102\boxed{3.68 \times 10^2}.

    b) 0.00006784

  10. Move the decimal point to the right until there is one non-zero digit before the decimal point.

    6.7846.784
  11. Count the number of places the decimal point was moved.

    Since it was moved 5 places to the right, the exponent of 10 is -5.

    6.784×10−56.784 \times 10^{-5}

    The standard form is 6.784×10−5\boxed{6.784 \times 10^{-5}}.

    c) 0.00321

  12. Move the decimal point to the right until there is one non-zero digit before the decimal point.

    3.213.21
  13. Count the number of places the decimal point was moved.

    Since it was moved 3 places to the right, the exponent of 10 is -3.

    3.21×10−33.21 \times 10^{-3}

    The standard form is 3.21×10−3\boxed{3.21 \times 10^{-3}}.

    d) 458754

  14. Move the decimal point to the left until there is one non-zero digit before the decimal point.

    4.587544.58754
  15. Count the number of places the decimal point was moved.

    Since it was moved 5 places to the left, the exponent of 10 is 5.

    4.58754×1054.58754 \times 10^5

    The standard form is 4.58754×105\boxed{4.58754 \times 10^5}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp